As described in above noted prior U.S. patents, with the use of head clamps for positioning a patient's head for neurosurgery or other cranial surgery, it is necessary to provide a rigid support for the head and one which can be easily adjusted to allow access by the surgeon to selected portions of the head of the patient during an operation. To this end, my prior structures have provided three articulated arms each with locking levers so that once the head of a patient has been placed in a position as desired by the surgeon, the head can be locked in place. With my structure, selecting any position in space is a continuously variable, analog function. Also, during surgical operations, it is important that the stability and rigidity of the head supporting structure be assured once the position selection has been made. In the past, use of a number of types of head support structures has proven inadequate in terms of the possibility of accidental release of the support structure during a medical procedure. While the locking mechanisms of my prior patents noted above have lessened this possibility, there is a need for a head bracket support that will achieve rapid and secure locking of the head bracket in place without the possibility of rotation of the bracket relative to its support or release of the bracket.